Jed Sullivan: Thought you might get a kick out of this hexomino
wine rack design,
assuming you haven't seen it before. [It's unfortunately not a complete set.]

Herding cats and other metal puzzles.

A new version of Dai Nagata's Cat
Packing Puzzle has been released by Bits and Pieces. Puzzlemaster.ca recently
released a combined set of three of the best Cast puzzles: Loeuf,
Radix, Disk. Pentangle has
also started carrying the Cast lineof metal puzzles.

Chess Tasks

Itamar Faybish: You may be familiar with chess compositions which are often
very ingenious and beautiful. These compositions are judged on how beautiful
they are, how they implements certain ideas, etc. These kinds are nice, but not
always easy to participate as there are really some very strong composers. The
new type is one based on certain mathematical properties that one has to either
maximize or minimize. The incredible - or not - thing about these is that the
actual compositions that comes out of it, as one gets higher "scores",
becomes more beautiful and subtler. Thus joining math & chess in a happy
wedding. [Itamar's site has
good links to other competitions.]

Andrew Clarke: I've just started a new page based on pieces formed by adding
to the square tetromino. It's at 4sqplus.htm.
Some of the sets are quite interesting and allow for multiple rectangle as well
as multiple simial figure constructions. Some of the multiple rectangles will
be quite hard to find if not impossible.

The Game of Trinim

jjartus: I wish to call your attention to the game called Trinim.
Numerous questions are unsolved, for instance which is the exact number of different
(non equivalent) starting configurations for each size? (rotations, symmetries,
color rotations and exchanges(g -> b -> r), are equivalent). There is a
rough estimate for n=5. Can a general formula be written for any allowed size?
The game is very complex, and there is so far no perfect player, human or computer.
Which are the winning strategies? Is there a simple way to determine whether
a board is a winner or a loser for a perfect player, aside from brute force
tree analysis? The game is played currently with 3 colors, but games with another
number of odd colors are possible.

Pi curiousity

Alvy: Hi! While playing with the "Pi
Phone Number Search Engine", one of my readers found this in Pi,
I don't know if it's already known, but for sure it's a number curiosity: "The
number 2424242 was found starting at position 242421 to the right of the decimal
point of Pi." [You can also read the original
post in Spanish in his blog.]

I had the pleasure of meeting David Krumholtz, Dr. Gary Lorden, Cheryl Heuton,
Nick Falacci, Andrew Black, Bill Nye, and Keith Devlin at the recent AAAS conference.
The coolest moment was a discussion with Bill
Nye and Andrew Black over a plate
of water and pepper as a possible moment in the show, and Bill Nye talking about
how he first saw the experiment while watching the original Mr. Wizard, then
following up with a wicking experiment. I shoulda brought a tape recorder with
me. David talked about the challenges about portraying a math genius and how
honored he is to be the face of promoting mathematics. Cheryl and Nick discussed
the steps of getting the show made in the first place, and the unexpected successes
they had every step of the way (the show now being #15). Gary Lorden talked about
some of the actual math in the show, and showed many clips from the show, pointing
out various items even I missed. Fun stuff. Here's a
different Numb3rs article,
from Zap2it.

Christopher Bird: Consider the sequence of 'number' equations. The largest possible
'number' equation in this sequence where solutions are still possible is S+E+V+E+N+T+E+E+N
= 17. This leaves a small set of solutions. However, when N+O+U+G+H+T = 0 is included,
we get a unique solution for each and every variable
used in the problem.

The furthest in the Greek alphabet that we can go where solutions are still possible
is T+A+U = 19 (19th letter). This leaves a small set of solutions. However, when
the final letter in the 24-letter Greek alphabet O+M+E+G+A = 24 is included, then,
once again, we would be left with only one and an unique solution for each and
every variable used in the problem.

An even more difficult problem than the Greek Alphabet set of equations is the
set concerning the NATO Phonetic Alphabet, which is most commonly used in radio
communication. Amazingly, even though we have a full set of 26 equations (one for
every letter of the alphabet), we nevertheless have an unique solution to each
and every letter-variable from A to Z (all 26 letters are represented, making this
a classic problem).

Hex-a-hop is an excellent
free puzzle game by Tom Beaumont. Basically, on small boards, you hop around
to destroy green tiles. Very simple conceptually, but very attractively laid
out, free, and filled with ingenious puzzle miniatures.

Deflexion

Deflexion is an interesting game of
lasers and mirrors. It's a physical board game.

Eric Solomon is the inventor of Black Box, the original deflection game, and
he has a great java site. And he's a regular contributor here, so I feel obligated
to mention him after two other deflection games.

A Combinatoric Question

Puzzleup has started a second year of
weekly puzzles. The ten countries puzzle given this week is quite nice.

The Griddle Site

Dave Millar, a frequent contributor here, has launched a puzzle-of-the-day
site called The Griddle, devoted to grid-type puzzles.

About a year ago, across the hallway from me, MathWorld teammember
John Renze managed to get a program working that proved a new Fibonacci Prime.
Now, that method is "An
Algebraic Approach to Primality Proving", and it's getting increasing attention
as a breakthrough.

Fractal Jigsaw

M. Oskar van Deventer: A couple of weeks ago, I wrote you about the Fractal
Jigsaw. Recently, I made a prototype on the laser cutter of Peter Knoppers. The
puzzle is a quite powerful optical illusion. When you take out a big piece, and
put it next to the hole, it is very clearly visible. When you give it a tiny
push to make it drop into the hole, suddenly the piece
completely disappears,
hidden in the fractal pattern.

Nick Baxter invites US residents to try out for the World
Sudoku Championship. Get a stopwatch ready, then head on over to that link.
You'll be able to download an excellent selection of variety Sudoku puzzles.
To possibly join the US team, write down your solving times. Then enter those
times in the registration form. If you're one of the fastest solvers, you'll
be given an opportunity to pay for your own flight and hotels in Italy, for
the World Championship.

Fried Okra Perplexities

A new puzzle at Puzzle Beast involves moving
plates of Okra and other goodies. It can be surprisingly difficult to get
hot okra, when the plate is large.

Oskar's Jukebox

Oskar van Deventer has added a new puzzle at Click Mazes, Oskar's
Jukebox.
You just have to put coins into the machine. How hard could it be?

Wolfram Technology Guide

The Wolfram
Technology Guide caught me completely unawares -- I didn't find out about
it until it got mentioned in Nikkei Science, the Japan version of Scientific
American. There are some interesting Flash demos of mathematical things
even I didn't know about. After watching several, I eagerly clicked on Sparse
Arrays, to see the zippy flash demo for that. Alas, just a chart there.

Intersecting Diagonals

Take a regular polygon, and draw all the diagonals. Other than at the center,
what's the most lines that can meet at a point? The answer is in a recent paper
by Bjorn Poonen
and Mike Rubinstein.

Planar Distance Graphs

In this month's Math Magic, Planar
Distance Graphs are the main focus. One problem for this month -- what
is the smallest planar graph that has edges of length 1, 2, and 3 connected
to every vertex? Here's another problem -- a graph with unit edges, three edges
at every vertex, and no triangles. If you can solve that, head over to Math
Magic and share your skills.

I've long wanted to make a mathematically perfect card deck. Now, a basic card
deck is 4x13, basically. Not really much better than 5x12, or 4x14. The game
of Set is 3^4. Why not 4^3? Well, no-one will be able to top the Hoffman-Singleton
graph for mathematical properties. And now, it's a card
deck. I'll be giving away 250 copies to attendees of G4G7. Another 250 copies
I'm selling here, for $10 each. If you'd like to reserve a deck, click on the
PayPal button on bottom of the left column. Feel free to add a donation if you
like my site.

Numb3rs article on MathTrek

The latest MathTrek mentions
my involvement with Numb3rs. Ivars should have also mentioned Michael Trott and
Eric Weisstein.

Fractal Tiling Goodness

Master tessellator Robert Fathauer has added some beautiful new pages about Fractal
Tilings.

TpX Vector Program

TpX, one of my favorite free vector programs, just came out with version Tpx
1.3. I just recently learned that it can accept TeX input in its diagrams.

I was at the bookstore earlier today, and saw about 30 near-identical Sudoku
books. Bob Harris is doing stuff more interesting than anything currently findable
in the stores. Recently, he proved that n-1 clues
are sufficient for any n-sized
geometric sudoku.

Rodney Mason -- Ed, I enjoyed this book so much. Thank You. I liked it
so much I converted it to PDF format with bookmarks so it is a little easier
to read and find the answers. Please feel free to post
the pdf (40Meg PDF) on your Math site
or do what ever you want to with it.

16 Clue, 2-solution Sudoku

In 2005, Gordon Royle compiled many 17-clue
Sudoku with unique solutions.
Gordon a careful analysis of them, and isolated a 16-clue Sudoku with exactly
two solutions. So far, this is the only 16-clue Sudoku found with just
2 solutions. Is there another that isn't a trivial variant of this one?

David Millar had an idea for some new chess pieces. Here is one of them, the
BullRider. He asks how many moves are needed for the BullRider to capture the
Black King. Not too hard. What other games and puzzles are possible with this
piece?

I'll be at the Joint Math
Meeting in San Antonio, Jan 12-15. I'll be at the
Wolfram Research booth, along with Eric Weisstein and Michael Trott. Feel free
to stop by to see me, if you're there. The organizers have put a Gallery
of Mathematical Art online which is well worth a look.

Ryohei Miyadera, Daisuke Minematsu and Munetoshi Sakaguchi present a problem:
given the below pieces of chocolate, where the red triangle is very bitter. Two
players in turn break the chocolate (in a straight line along the grooves) and
eats the piece he breaks off. The player to leave his opponent with the single
bitter part is the winner. Describe the stratedy to ensure winning. They wrote
up an excellent PDF and Mathematica notebook with
the answer. Other good work they've done includes an analysis of Russian Roulette.

DROD: JtRH a game of the year

I wrote a column about DROD:
Journey to Rooted Hold - a great puzzle game
(which I completed!). I later learned that no less than 5 Math Olympiad finalists
were all DROD fans. After winning a spot in the top
10 Indie Games of the Year,
DROD got coverage on Penny Arcade, Slashdot, GameTunnel, and Adrenaline Vault,
and other sites, which allowed DROD to have a great start for 2006. They recently
had a contest on Hermetic
Puzzles which is well worth a look.

The Neighborly Square

From Bernardo Recaman: Place the numbers 1 to 16 in the cells of a 4 x 4 grid
so that no cell is the sum of a subset of its (up to 8) neighbours. Thus, 5
couldn't have both 1 and 4 as neighbors, or both 2 and 3 as neighbors. Answer
and Solvers.